Discovering state-of-the-art quantum circuits with large language models

Creating efficient quantum algorithms is hard because every operation must be reversible and the basic building blocks consume a lot of resources. This work tackles those problems with an evolutionary system that pairs a large language model (LLM) with an independent evaluator. The LLM generates new quantum‑circuit designs, and the evaluator checks whether they are correct and rates their efficiency. The authors tested the approach on eight different tasks, including numerical computation, quantum chemistry, optimization, quantum simulation, and number theory. In seven of the eight tasks, the system discovered circuits that use far fewer Toffoli gates and qubits than the best existing designs. For the remaining task, it found a

new reversible architecture for prime‑field modular inversion. This architecture incorporates “divsteps,” a classical algorithm previously thought impractical for reversible integer arithmetic, and it improves the Toffoli‑qubit trade‑off. For M.Tech researchers, the paper offers a solid foundation for exploring LLM‑driven heuristic searches in tightly constrained design spaces, though building the circuits in practice will require a reliable quantum verification environment and access to capable LLM APIs.

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